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Symplectic duality and implosions

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TLDR
In this article, the authors discuss the universal hyperkahler implosion for various groups and present candidates for the symplectic duals of the universal HH implosions.
Abstract
We discuss symplectic and hyperkahler implosion and present candidates for the symplectic duals of the universal hyperkahler implosion for various groups.

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Connecting 5d Higgs Branches via Fayet-Iliopoulos Deformations

TL;DR: In this article, the geometry of the Higgs branch of 5D superconformal field theories is transformed under movement along the extended Coulomb branch by using a magnetic quiver to establish a local version of mirror symmetry.
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Higgs branches of U/SU quivers via brane locking

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Higgs Branches of U/SU Quivers via Brane Locking.

TL;DR: In this article, the authors solved the problem of computing the Higgs branch of linear quivers with 8 supercharges and with both unitary and special unitary gauge nodes using the concept of magnetic quivers, where components of $\mathcal{H}$ are described as 3d Coulomb branches.
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Some Open Questions in Quiver Gauge Theory

TL;DR: In this article, Gasparim et al. collected a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry.
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Book

Representation theory and complex geometry

TL;DR: This book discusses K-Theory, Symplectic Geometry, Flag Varieties, K- theory, and Harmonic Polynomials, and Representations of Convolution Algebras.
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Lie Group Representations on Polynomial Rings

TL;DR: In this paper, a group of linear transformations on a finite dimensional real or complex vector space X is considered as a G-module, and S is the sub-ring of all G-invariant polynomials on X.
Journal ArticleDOI

The construction of ALE spaces as hyper-Kähler quotients

TL;DR: On decrit la construction d'une famille particuliere de 4-varietes hyper-Kahler: les espaces asymptotiquement localement euclidiens ALE On decrit une 4-variiete de Riemann avec juste une extremite qui a l'infini ressemble au quotient R 4 /Γ de l'espace Euclidien R 4 par un groupe fini Γ d'identifications as mentioned in this paper.
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S-duality of boundary conditions in N=4 super Yang-Mills theory

TL;DR: In this paper, the S-duality of boundary conditions is closely related to mirror symmetry of three-dimensional gauge theories, and the IR behavior of large classes of quiver gauge theories.
Book ChapterDOI

Lie Group Representations on Polynomial Rings

TL;DR: In this paper, a group of linear transformations on a finite dimensional real or complex vector space X is considered as a G-module, and S is the sub-ring of all G-invariant polynomials on X.
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